topic 9

Question 1

electrons behave like a tiny bar magnet

Answer 1

due to intrinsic angular momentum of an electron (s)
- has magnetic moment (us)
- must be quantised

Question 2

the orbital angular momentum of an electron with l>0 leads to

Answer 2

a second source of atomic magnetic moment ul
- magnetic moment vectors oriented in opposite direction to angular momentum vectors from which they stem from
- must be quantised (values that make up equation are quantised)

Question 3

spin - orbit coupling

Answer 3

• magnetic interaction between quantised spin and orbital magnetic moments of an electron
• leads to total angular momentum J
• internal interaction = splitting

Question 4

Zeeman effect

Answer 4

• external interaction between an atom and an applied magnetic field that further spilts the energy of the levels into individual states

Question 5

in an applied magnetic field, B, energy of the magnetic moment associated with the total angular moment, uj, of an electron

Answer 5

changes
- change in energy depend on the relative orientation of the magnetic moment (quantised by Mj) and the direction of the applied field
- Zeeman effect

Question 6

hands rules involving spin - orbit coupling

Answer 6

• for a sub shell less than half full, lowest J = ground level
• for a sub shell more than half full, highest J = ground level
• for an exactly filled half - sub shell there is no spin - orbit coupling in ground state due to rules of maximum multiplicity

Question 7

how is the hole formalism (configuration of holes and electrons give rise to the same terms) effected by spin - orbit coupling

Answer 7

• the splitting term is reversed due to hunds 3rd rule and so pairs of electron configurations have different ground state level

Question 8

energy of level 2s+1L (term)

Answer 8

E_L,S,J = hcA( J(J+1) - L(L+1) - S(S+1)/ all divided by 2)
- A is spin - orbit coupling constant (cm^-1)

Question 9

coupling constant A

Answer 9

• increases with atomic number and scales roughly as A proportion to Z^4
• less than Half filled sub shell A>0 Such that E(J) increases as J increases
• more than half filled sub shell A<0 such that E(J) decrease as J increases

Question 10

lande interval rule

Answer 10

• for levels of the same term, the values of L and S are the same
• thus the energy spacing between levels J and J + 1
  = hcA (J + 1)

Question 11

selection rules

Answer 11

• change in J = 0, +/- 1
• change in S = 0
• change in L = 0, +/- 1 (provided change in l = +/- 1)
• chang in n = no restrictions
• change in Mj states = 0, +/- 1

Question 12

spin - orbit coupling spectral line splitting

Answer 12

• alkali metals where p electron of an electronically excited state relaxes to a lower s orbital, spin orbit coupling gives rise to important spectral feature
• look at strong line at 589 nm under high resolution, see doublet
• due to spin - orbit coupling
• down the alkali metal group the splitting increases with spin - orbit coupling constant ( A proportional to Z^4)
• doublet because line splitting from 2p3/2 to 2S1/2 and 2P1/2 to 2S1/2

Question 13

Zeeman effect equation

Answer 13

• E = -total angular momentum (uj) x applied magnetic field (B) = - modulus uj x modulus B x cos(theta)

Question 14

the stronger the applied field

Answer 14

the stronger the spectral line splitting